Radius selection and droplet unpinning in vapor-liquid-solid-grown nanowires

The requirements for steady nanowire growth under near-equilibrium conditions in the vapor-liquid-solid (VLS) method is examined with particular emphasis on the configuration of the liquid droplet. It is found that the final radius of a cylindrical wire is selected by the fixed volume of liquid V-L and the surface-energy ratio gamma(sl)/gamma(lv) but is independent of the solid-vapor energy gamma(sv). Existing models for growth, based on a balance of configurational forces at the triple junction, are shown to be consistent with the principle of maximal release of free energy. Gibbs's results on allowable contact angles at a sharp corner predict conditions on gamma(sl)/gamma(lv) and gamma(sv)/gamma(lv) for the existence of straight-wire growth. For parameter values that violate these conditions the droplet atop the wire is expected to unpin. A range of alternative configurations for the liquid exist and their relative energies are compared. In particular, it is found that for a certain region in parameter space-not extraordinary in VLS growth-a spherical cap of liquid is not in equilibrium and an annulus of liquid surrounding the wire is energetically preferred. This is suggestive of a possible instability during growth